Find the second Taylor polynomial, P2(x), for f(x)=excosx about x0=0.
((a)) Use P2(0.5) to approximate f(0.5). Find an upper bound on the error ∣f(0.5)−P2(0.5)∣ using the remainder term and compare it to the actual error.
((b)) Find a bound on the error ∣f(x)−P2(x)∣ good on the interval [0,1].
((c)) Approximate ∫01f(x)dx by calculating ∫01P2(x)dx instead.
((d)) Find an upper bound for the error in (c) using ∫01∣R2(x)∣dx and compare the bound to the actual error.